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- StudyBlue
- North-carolina
- University of North Carolina - Charlotte
- Mathematics
- Mathematics 2241
- Gordon
- 10.1 - 3D Coordinate Systems

Jason S.

We know that any point in the plane can be represented as an __________ of real numbers, where *a* is the *x*-coordinate and b is the *y*-coordinate

- ordered pair (
*a,b*) - ordered triple (
*a,b,c*)

ordered pair (*a,b*)

We represent any point in space by an _________ of real numbers.

- ordered pair (
*a,b*) - ordered triple (
*a,b,c*)

ordered triple (*a,b,c*)

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)

xy-plane

- x = 0
- y = 0
- z = 0

z = 0

xz-plane

- x = 0
- y = 0
- z = 0

y = 0

yz-plane

x = 0

y = 0

z = 0

x = 0

Octants

Octants are the 8 spaces that the coordinate planes create.

The first-octant is the octant in which all point coordinates are positive. There is no conventional numbering system for the remaining octants.

The first-octant is the octant in which all point coordinates are positive. There is no conventional numbering system for the remaining octants.

Octant I

- x > 0, y > 0, z < 0
- x > 0, y < 0, z > 0
- x > 0, y > 0, z > 0

3. x > 0, y > 0, z > 0

Octant II

- x > 0, y > 0, z < 0
- x < 0, y > 0, z > 0
- x > 0, y > 0, z > 0

2. x < 0, y > 0, z > 0

Octant III

- x > 0, y > 0, z < 0
- x < 0, y > 0, z < 0
- x < 0, y < 0, z > 0

3. x < 0, y < 0, z > 0

Octant IV

- x > 0, y < 0, z > 0
- x < 0, y > 0, z < 0
- x < 0, y < 0, z > 0

1. x > 0, y < 0, z > 0

In two-dimensional analytic geometry, the graph of an equation involving *x* and *y* is a _______ in R^{2}. In three-dimensional analytic geometry, an equation in *x*, *y*, and *z* represents a _______ in R^{3}

- curve; surface
- surface; surface

curve; surface

Octant V

- x > 0, y > 0, z < 0
- x < 0, y > 0, z < 0
- x < 0, y < 0, z > 0

1. x > 0, y > 0, z < 0

What surfaces in **R**^{3} are represented by the following equation, y = 5?

What surfaces in **R**^{3} are represented by the following equation, z = __3__?

- the set of all points in
**R**^{3}whose z-coordinate is__3__. - the set of all points in
**R**^{3}whose y-coordinate is__5__.

Represents the set {(x, y, z) | z = 3}, which is the set of all points in **R**^{3} whose z-coordinate is __3__.

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What surfaces in **R**^{3} are represented by the following equation, y = 5?

- the set of all points in
**R**^{3}whose z-coordinate is__3__. - the set of all points in
**R**^{3}whose y-coordinate is__5__.

Represents the set {(x, y, z) | y = 5}, which is the set of all points in **R**^{3} whose y-coordinate is __5__.

Distance Formula in 3D

Distance |P_{1}P_{2}| between points P_{1}(x_{1},y_{1},z_{1}) & P_{2}(x_{2},y_{2},z_{2}) is

Distance |P

- |P
_{1}, P_{2}| = √((x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}+(z_{2}-z_{1})^{2}) - |P
_{1}, P_{2}| = √((x_{2}-x_{1})^{2}−(y_{2}-y_{1})^{2}−(z_{2}-z_{1})^{2})

|P_{1}, P_{2}| = √((x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}+(z_{2}-z_{1})^{2})

Distance between two points P(x_{1},y_{1},z_{1}) and Q(x_{2},y_{2},z_{2}) in R^{3}:

True or False

- d = √(x
_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}+(z_{2}-z_{1})^{2}

True or False

True

Equation of a sphere of radius r centered at C(x_{0},y_{0},z_{0}):

- (x
_{0}-x)^{2}-(y_{0}-y)^{2}-(z_{0}-z)^{2}= r^{2}

True or False

False

**(x-x**_{0})^{2}+(y-y_{0})^{2}+(z-z_{0})^{2} = r^{2}**or****x**^{2} + y^{2} + z^{2} = r^{2}

Equation for the coordinates of a midpoint M:

- M • ((x
_{1}+x_{2}/2),(y_{1}+y_{2}/2), z_{1}+z_{2}/2)

True or False

True

Equation of a sphere with center *C*(*h, k, l*) & radius *r*

- (
*x*−*h*)^{2}+(*y*−*k*)^{2}+(*z*−*l*)^{2}=*r*^{2} - (
*x*−*h*)^{2}−(*y*−*k*)^{2}−(*z*−*l*)^{2}=*r*^{2} - (
*x*−*h*)^{3}−(*y*−*k*)^{3}−(*z*−*l*)^{3}=*r*^{5}

(*x*−*h*)^{2}+(*y*−*k*)^{2}+(*z*−*l*)^{2} = *r*^{2}

^{}

also: *x*^{2} + *y*^{2} + *z*^{2} = *r*^{2} if the is the origin *O*

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